The entanglement entropy is one of the most important quantities which measure the quantum entanglement among different degrees of freedom of a quantum mechanical systems [1]}, [2]}. In fact, EE has emerged as a valuable tool to probe the physical information in quantum systems. To define the EE, we consider a quantum system which is described by the pure state \(\vert \psi \rangle \)  and density matrix \(\rho =\vert \psi \rangle \langle \psi \vert \) . By dividing the total system into two subsystems \(A\)  and its complement \(\bar{A}\) , the total Hilbert space becomes factorized \(\mathcal {H}_{tot}=\mathcal {H}_A\otimes \mathcal {H}_{\bar{A}}\) . The reduced density matrix for the subsystem \(A\) , \(\rho _A\) , is obtained by tracing out the degrees of freedom in the complementary subsystem, \(\rho _A=Tr_{\bar{A}}(\rho )\) . The entanglement between subsystems \(A\)  and \(\bar{A}\)  is measured by the entanglement entropy which is a non-local quantity and defined as the Von-Neumann entropy of the reduced density matrix \(\rho _A\) 

SA=-Tr(A A).

In the framework of the gauge/gravity duality, the RT-proposal is a remarkably simple prescription to compute entanglement entropy in terms of a geometrical quantity in the bulk [3]}, [4]}. According to the RT-prescription, the HEE is given by

SA=Area(A)4GN(d+2),

where \(G_N^{(d+2)}\)  is the \((d+2)\) -dimensional Newton constant. \(\Gamma _A\)  is a codimension-2 minimal hypersurface in the bulk (RT-surface) whose boundary \(\partial \Gamma _A\)  coincides with the boundary of region \(A\) , \(\partial \Gamma _A=\partial A\) . We also require \(\Gamma _A\)  to be homologous to region \(A\) . It can be shown that the EE for two disjoint subsystems \(A\)  and \(B\)  satisfies the so-called strong subadditivity condition \(S_A+S_B\geqslant S_{A\cup B}+S_{A\cap B}\)  [5]}.
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